In a brief, multi-section teshuva from 1957, Rav Moshe Feinstein quickly rules on several issues concerning the three weeks:
1) A person is allowed to sing zemirot on the Shabbat preceding Tisha B'Av (Shabbat Chazon), even if the person is not accustomed to singing zemirot on a regular Shabbat. This is due to the fact that kavod Shabbat overrides any of our customs for the three weeks. Similarly, one can eat meat during seudah shlishit on that week, even if Tisha B'Av is that night.
2) A person can shave or take a haircut on the night of the 17th of Tammuz if it is absolutely necessary (since even though the date has arrived, the fast does not begin until the morning).
3) A person can buy meat during the nine days for consumption after the nine days, and does not have to worry that someone who sees him will think that he intends to eat it now (marit ayin).